Randomised
Social
Choice
Theory

This work contains a formalisation of basic Randomised Social Choice,
including Stochastic Dominance and Social Decision Schemes (SDSs)
along with some of their most important properties (Anonymity,
Neutrality, ex-post- and SD-Efficiency, SD-Strategy-Proofness) and two
particular SDSs – Random Dictatorship and Random Serial Dictatorship
(with proofs of the properties that they satisfy). Many important
properties of these concepts are also proven – such as the two
equivalent characterisations of Stochastic Dominance and the fact that
SD-efficiency of a lottery only depends on the support. The entry
also provides convenient commands to define Preference Profiles, prove
their well-formedness, and automatically derive restrictions that
sufficiently nice SDSs need to satisfy on the defined profiles.
Currently, the formalisation focuses on weak preferences and
Stochastic Dominance, but it should be easy to extend it to other
domains – such as strict preferences – or other lottery extensions –
such as Bilinear Dominance or Pairwise Comparison.